(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{3xy}{3x^2+7y^2}[/tex], y(1)=1

Express it in the form F(x,y)=0

3. The attempt at a solution

I'm not sure where I'm going wrong. I let v=y/x,

v+x[tex]\frac{dv}{dx}[/tex] = [tex]\frac{3x^2v}{3x^2+7x^2v^2}[/tex]=[tex]\frac{x^2(3v)}{x^2(3+7v^2)}[/tex]= [tex]\frac{3v}{3+7v^2}[/tex]

[tex]\Rightarrow[/tex] x[tex]\frac{dv}{dx}[/tex] = [tex]\frac{-7v^3}{3+7v^2}[/tex]

I think that's right so far, but I'm not entirely sure. Here is where I feel something is going wrong.

[tex]\frac{3+7v^2}{-7v^3}[/tex] [tex]\frac{dv}{1}[/tex] = [tex]\frac{dx}{x}[/tex]

[tex]\frac{3}{14v^2}[/tex]-ln(abs(v))=ln(x)+c

[tex]\frac{3x^2}{14y^2}[/tex]-ln(abs([tex]\frac{y}{x}[/tex]))-ln(x)+c=0

c=3/14 since y(1)=1

And therefore,

F(x,y)= [tex]\frac{3x^2}{14y^2}[/tex]-ln(abs([tex]\frac{y}{x}[/tex]))-ln(abs(x))-[tex]\frac{3}{14}[/tex]=0

The answer isn't right. If someone could help me find where I've gone wrong, it would be very appreciated. Sorry about the scripting. I'm not skilled at it yet, but, hopefully it's easy enough to read. Thank you!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: First Order Homogeneous Equations

**Physics Forums | Science Articles, Homework Help, Discussion**